Height and Distance — NDA Mathematics PYQs

Consider the following for the two (02) items that follow :
The top ($M$) of a tower is observed from three points $P$, $Q$ and $R$ lying in a horizontal straight line which passes directly along the foot ($N$) of the tower. The angles of elevations of $M$ from $P$, $Q$ and $R$ are $30°$, $45°$ and $60°$ respectively. Let $PQ=a$ and $QR=b$.

What is $PN$ equal to?

Consider the following for the two (02) items that follow :
The top ($M$) of a tower is observed from three points $P$, $Q$ and $R$ lying in a horizontal straight line which passes directly along the foot ($N$) of the tower. The angles of elevations of $M$ from $P$, $Q$ and $R$ are $30°$, $45°$ and $60°$ respectively. Let $PQ=a$ and $QR=b$.

What is $MN$ equal to?

A man at $M$, standing $100$ m away from the base ($P$) of a chimney of height $50$ m, observes the angle of elevation of the highest point ($Q$) of the smoke to be $45°$. The highest point of the chimney is at $R$. Further $P$, $R$ and $Q$ are in a straight line and the straight line is perpendicular to $PM$. What is the angle $RMQ$ equal to?